Bootstrap tests for variance components in generalized linear mixed models

In many applications of generalized linear mixed models to clustered correlated or longitudinal data, often we are interested in testing whether a random effects variance component is zero. The usual asymptotic mixture of chi-square distributions of the score statistic for testing constrained variance components does not necessarily hold. In this article, the author proposes and explores a parametric bootstrap test that appears to be valid based on its estimated level of significance under the null hypothesis. Results from a simulation study indicate that the bootstrap test has a level much closer to the nominal one while the asymptotic test is conservative, and is more powerful than the usual asymptotic score test based on a mixture of chi-squares. The proposed bootstrap test is illustrated using two sets of real-life data obtained from clinical trials. The Canadian Journal of Statistics © 2009 Statistical Society of Canada Dans plusieurs applications des modeles lineaires mixtes generalises aux donnees correlees en grappe ou aux donnees longitudinales, nous sommes souvent interesses a voir si la composante de la variance reliee aux effets aleatoires est nulle ou non. La distribution asymptotique standard, correspondant a un melange de distributions du khi carre, des statistiques de type score utilisee pour tester la composante de la variance contrainte n'est pas necessairement valide. Dans cet article, l'auteur propose et etudie un test de reechantillonnage parametrique qui semble etre valide si nous nous basons sur son niveau de confiance sous l'hypothese nulle. Des simulations indiquent que le test de reechanillonnage a un niveau plus pres de la valeur nominale tandis que le test asymptotique est conservateur. De plus, il est plus puissant que celui base sur le melange de distributions du khi carre. L'utilisation de ce test de reechantillonnage est illustree a l'aide de deux jeux de donnees provenant d'essais cliniques. La revue canadienne de statistique © 2009 Societe statistique du Canada

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